Bath engineering of a fluorescing artificial atom with a photonic crystal

A quantum emitter decays due to vacuum fluctuations at its transition frequency. By virtue of the entwined nature of dissipation and fluctuations, this process can be controlled by engineering the impedance of the environment. We study how the structured vacuum environment of a microwave photonic crystal can be used for bath engineering of a transmon qubit. The photonic crystal is realized by a step-impedance transmission line which suppresses and enhances the quantum spectral density of states akin to a Purcell filter. We demonstrate a bath engineering protocol upon driving an emitter near the photonic band edge that allows dissipation to produce non-trivial steady-states.